Neutrino Model of Dark Energy
Yong-Yeon Keum
Academia Sinica/Taiwan
Mujuresort, Feb./16-19/2005
ContentsContents
Experimental evidence of accelerating universe
Candidates of Dark Energy
Neutrino Model of Dark Energy
Lesson from FKNW model (An example of interacting dark matter and
dark energy model)
Experimental Observations(1)Experimental Observations(1)
Experimental Observation(2)Experimental Observation(2)
Our universe is flat, accelerating. The dominance of a dark energy component with negative
pressure in the present era is responsible for the universe’s accelerated expansion.
Accelerating UniverseAccelerating Universe
Cosmological Constant Problem: Why is the energy of the vacuum so much small ?
Dark Energy Puzzle: What is the nature of the smoothly-distributed, persistent
energy density which appears to determine the universe.
Coincidence Scandal: Why is the dark energy density approximately equal to
the matter density today
Candidates of Dark EnergyCandidates of Dark Energy
(A) Cosmological Constant (consntant)(B) Dynamical Cosmological Constant
(Time-dependent; Quintessence field)
(C) Modified Gravity (Modified Friedmann Eq.)
(A) Cosmological Constant(A) Cosmological Constant
Typical scale :
Hence a new energy density scale is too low
from the particle physics point of view.
2 42 20 (10 )H GeV
22 2 40
0 )8 P
N
HM H eV
G
4)particle GeV
8 NG g G T
Cosmological constant problemCosmological constant problem
Many different contributions to vacuum energies:
(a) QCD ~ Digression to particle physics and the vacuum energy
problem
(b) EW physics ~ (c) GUT ~
(d) SUSY ~
All these contributions should conspire to cancel down to . Extreme fine tuning !!!
4(1 )GeV
16 4(10 )GeV3 4(10 )GeV
4 4(10 )GeV
2 4(10 )GeV
( B ) Quintessence( B ) Quintessence
Quintessence = dark energy as a scalar field = dynamical cosmological constant
No evidence for evolving smooth energy, but attractive reasons for dynamical origins !
(a) why small, why not zero, why now ??? (b) suggest the physical cosmological evolution. Canonical quintessence:
2
3(1 )
1, ( )
2( )
3 0, 3 ( ) 0
( 1)
K V
dVH H p
d
p a
Quintessence (2)Quintessence (2)
If potential energy dominates over the kinetic energy
This type of potential is not so easy to stabilize w.r.t.quantum loop corrections.
2 2
0
0 4 40
1 1( ); ( )
2 2
1 ( )
1 1( ) ( ) [ 3(1 ) ]
2 2
(10 )
P
P c
V p V
paccelerating
V V ExpM
M V eV
( C ) Modified Gravity( C ) Modified Gravity Newtonian Cosmology: Gravitational Force law determines the
evolution
Combining the above eqs:
Moreover, E = constant and decelleration !!
2
34
3( )
N
F MR G
m R
M R
R a t r
4( )
3 N
aG t
a
33
2/3
4 1
3
0
E M Ra
a t a
Modified ForceModified Force
For simplicity g=1
(1) Early times t << tc so that
matter domination, no acceleration
(2) Later time, t > tc when
Accelerated expansion !!!
22
2
3
( )
4( ) ,
3
( ) 0
Nc
N c
G MFR m Rg R
m R
R G R m g R R
d a
2 2/34, ~
3N c NG m R G R a t
2 2 2, ~ , ~ 0!!!cm tN c c cG m R m R a e a m
Neutrino Model of Dark EnergyNeutrino Model of Dark Energy
Cosmological constant:
What physics is associated with this small energy scale ?? It is clearly a challenge to understand dynamically how the
small energy scale associated with dark-energy(DE) density aries and how it is connected to particle physics.
33 2 2 40
0
4 4 )
( ) 1
(1.5 0.1) 10 , )
N DE N DE
DE DE
DE P o
G G p p
p
Since H x eV M H eV
E eV
Interacting dark energy modelInteracting dark energy model
FNW scenarioFNW scenario
Fardon, Nelson and Weiner suggested that tracks the energy density in neutrinos
The energy density in the dark sector has two-components:
The neutrinos and the dark-energy are coupled because it is assumed that dark energy density is a function of the mass of the neutrinos:
DE
( )m m n
dark DE
( )DE DE n
Since in the present epoch, neutrinos are non-relativistic (NR),
Assuming dark-energy density is stationary w.r.t. variations in the neutrino mass,
Defining
( )dark DEm n m n m
( )0
3 ( )
dark DE mnm m
H p
,
1
dark
dark
dark dark DE DE
dark DE
p
p p p
m n m n
m n